Abstracts - KTH Mechanics

Flow Separation from a Free Surface
Dominated BySurface Tension
I. R. Williams ∗
An experiment is currently underway where the flow past capillary surface profiles
is investigated. The range of surface shapes that are possible is of considerable
interest. The experiment consists of a fully wetted upper reservoir with an adjustable
aperture at its base. The aperture can be circular or linear. Fluid falls a distance of
the order of the capillary length (4mm) into a lower reservoir. The Reynolds number,
aperture size and jet length are varied. Profiles are possible where high surface curvature
occurs or where thickness of the jet becomes of the order of the viscous length
scale. Numerical results for the flow past the same two-dimensional surface profiles
are calculated using the adaptive mesh refinement Navier-Stokes solver.
Boundary layer theory has mainly found application for flow past no-slip surfaces
with very little attention being given to free-surface problems. Early work by Moore 1 .
and Harper 2 looked at boundary layer flow past ellipsoidal bubbles and showed that
the flow can detach from the surface of the bubble if the aspect ratio is sufficient. More
recent numerical work (see Magnaudet and Eames review 3 ) confirms flow separation
from bubbles and shows that separation only occurs for a certain range of Reynolds
number. This experiment aims to provide further details of flow separation from
free surfaces. Also, by using an adaptive mesh Navier-Stokes solver 4 , details of the
boundary layer can be resolved within reasonable computational time.
∗ Department of Mathematics, University of Bristol, U.K.
1 D.W.Moore, J. Fluid Mech. 23, 749-766 (1965).
2 J.F.Harper, Adv. Appl. Mech 12, 59-129 (1972).
3 Magnaudet and Eames, Annu. Rev. Fluid Mech. 32, 659-708 (2000).
4 Popinet, J. Comput. Phys. 190, 572-600 (2003).
Figure 1: Photograph from a preliminary experiment showing flow separation from
an axi-symmetric surface profile. Reynolds Number 300, Weber Number 0.5
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